Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called \textbf{High-Order Implicit Neural Representations (HOIN)}. By refining the traditional cascade structure to foster high-order interactions among features, HOIN enhances the model's expressive power and mitigates spectral bias through its neural tangent kernel's (NTK) strong diagonal properties, accelerating and optimizing inverse problem resolution. By analyzing the model's expression space, high-order derivatives, and the NTK matrix, we theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB improvements in most inverse problems, establishing a new state-of-the-art recovery quality and training efficiency, thus providing a new general paradigm for INR and paving the way for it to solve the inverse problem.

翻译：隐式神经表示（INR）在逆问题求解中面临日益严重的谱偏差问题，导致解过于平滑。针对此问题，我们提出了一种通用的逆问题处理框架——**高阶隐式神经表示（HOIN）**。通过改进传统级联结构以增强特征间的高阶交互，HOIN提升了模型表达能力，并利用其神经正切核（NTK）的强对角特性缓解谱偏差，从而加速并优化逆问题求解。通过分析模型的表达空间、高阶导数及NTK矩阵，我们从理论上验证了HOIN的可行性。HOIN在多数逆问题上实现了1至3 dB的性能提升，创下了新的最优先恢复质量与训练效率，为INR提供了新的通用范式，并为其解决逆问题铺平了道路。